Ramsey correlation spectroscopy with phase cycling using a single quantum sensor
Magnetic spectroscopy at the nanoscale provides unique insights into material properties and dynamics, with quantum sensors like nitrogen-vacancy (NV) centers being ideally suited for these scales. However, detecting low-frequency signals remains a challenge due to finite coherence times ($T_2^*$), as signals oscillating slower than $1/T_2^*$ decay before sufficient phase accumulation occurs. We present RESOLUTE (Ramsey corrElation SpectroscOpy puLse seqUence wiTh phasE cycling), a protocol that overcomes these limitations by combining Ramsey measurements with correlation spectroscopy. By storing accumulated phase as a population imbalance during a correlation period ($T_\mathrm{corr} < T_1$) between two sensing periods, RESOLUTE generates an effective coherence time $T_2^p > T_2^*$. This shifts the frequency-matching condition to the correlation time, enabling detection in the previously inaccessible spectral region between $1/T_1$ and $1/T_2^p$. We experimentally demonstrate an extension of the effective coherence time from $T_2^* = 0.38\,\mu s$ to $T_2^p = 5.1\,\mu s$, surpassing Hahn Echo measurements. The technique successfully detects $^{13}$C nuclear spin Larmor precession at fields as low as 49$\,$G ($\sim$50$\,$kHz). We further provide theoretical insight using Fisher information to characterize RESOLUTE's frequency estimation capabilities compared to existing protocols. Finally, by integrating adiabatic pulses and phase cycling, we demonstrate robust spin control and effective DC signal extraction. These advancements provide enhanced sensitivity to weak dipolar interactions, essential for single-molecule imaging and quantum sensing applications.